Highest Common Factor of 189, 217, 498 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 189, 217, 498 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 189, 217, 498 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 189, 217, 498 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 189, 217, 498 is 1.
HCF(189, 217, 498) = 1
HCF of 189, 217, 498 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 189, 217, 498 is 1.
Highest Common Factor of 189,217,498 is 1
Step 1: Since 217 > 189, we apply the division lemma to 217 and 189, to get
217 = 189 x 1 + 28
Step 2: Since the reminder 189 ≠ 0, we apply division lemma to 28 and 189, to get
189 = 28 x 6 + 21
Step 3: We consider the new divisor 28 and the new remainder 21, and apply the division lemma to get
28 = 21 x 1 + 7
We consider the new divisor 21 and the new remainder 7, and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 189 and 217 is 7
Notice that 7 = HCF(21,7) = HCF(28,21) = HCF(189,28) = HCF(217,189) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 498 > 7, we apply the division lemma to 498 and 7, to get
498 = 7 x 71 + 1
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 1 and 7, to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 498 is 1
Notice that 1 = HCF(7,1) = HCF(498,7) .
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Frequently Asked Questions on HCF of 189, 217, 498 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 189, 217, 498?
Answer: HCF of 189, 217, 498 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 189, 217, 498 using Euclid's Algorithm?
Answer: For arbitrary numbers 189, 217, 498 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
